Matrices, Digraphs, and Determinants

Maybee, John S.; Olesky, D.D.; Driessche, P. van den; Wiener, Gerry

doi:10.1137/0610036

Cited by 65 publications

(50 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof uses the following theorem, stated for tree graphs in [9] and for general digraphs in [11], which we restate here for digraphs D(W ) with tridiagonal W . …”

Section: Let D(a(i)) Be the Associated Digraph Obtained By Deletingmentioning

confidence: 99%

Group inverses of matrices with path graphs

Catral¹,

Olesky²,

Driessche³

2008

ELA

View full text Add to dashboard Cite

Abstract.A simple formula for the group inverse of a 2 × 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal (which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of such matrices are given. An extension of the graph-theoretic description of the group inverse to singular matrices with tree graphs is conjectured.

show abstract

“…The proof uses the following theorem, stated for tree graphs in [9] and for general digraphs in [11], which we restate here for digraphs D(W ) with tridiagonal W . …”

Section: Let D(a(i)) Be the Associated Digraph Obtained By Deletingmentioning

confidence: 99%

Group inverses of matrices with path graphs

Catral¹,

Olesky²,

Driessche³

2008

ELA

View full text Add to dashboard Cite

show abstract

“…The inverse of the Gaudin-matrix can be expressed in terms of its principal minors and sequences of its matrix elements [11,62] by the formula as follows:…”

Section: Jhep03(2018)047mentioning

confidence: 99%

Exact finite volume expectation values of $$ \overline{\varPsi}\varPsi $$ in the massive Thirring model from light-cone lattice correlators

Hegedűs

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operatorΨΨ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operatorΨΨ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardotype series representation of the expectation values are also checked.

show abstract

“…The introduction of the weighted adjacency matrix W to describe the walks on a graph goes back to the 60's. In [11,18], the spectral properties of a graph are investigated via the determinant and characteristic polynomial of W. Digraphs also provide a useful tool to compute the determinant and minors of sparse matrices, as discussed in [16]. For general results on spectral graph theory, we refer to [8,9].…”

Section: Introductionmentioning

confidence: 99%

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Espinasse

Rochet

2016

Graphs and Combinatorics

View full text Add to dashboard Cite

A walk in a directed graph is defined as a finite sequence of contiguous edges. Seeing the edges as indeterminates, walks are investigated as monomials and endowed with a partial order that extends to possibly unconnected objects called hikes. Analytical transformations of the weighted adjacency matrix reveal a relation between walks and self-avoiding hikes, giving rise to interesting combinatorial properties such as an expression of the number of ways to travel a walk in function of its self-avoiding divisors.

show abstract

Matrices, Digraphs, and Determinants

Cited by 65 publications

References 13 publications

Group inverses of matrices with path graphs

Group inverses of matrices with path graphs

Exact finite volume expectation values of $$ \overline{\varPsi}\varPsi $$ in the massive Thirring model from light-cone lattice correlators

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Contact Info

Product

Resources

About